308  Estimating the Cost of Capital Estimating the Cost of Equity The cost of equity is the central building block of the cost of capital. Unfor- tunately, it is also extremely difficult to measure. Academics and practitio- ners have proposed numerous models to estimate the cost of equity, but none have been reliable, especially at the company level. Even if a model could be agreed upon, accurately measuring the required inputs has also proven elu- sive. Consequently, deriving the cost of equity is far more difficult in practice than many core finance texts imply. With these hurdles in mind, we estimate the cost of equity in two steps: 1. Estimate market return. First, we estimate the expected return on the en- tire stock market. Although a particular company will not necessarily have the same cost of capital as the market as a whole, the market return provides a critical benchmark for judging how reasonable estimates of cost of equity for individual companies are. 2. Adjust for risk. We next adjust for company risk using one of two well- known models, the capital asset pricing model (CAPM) and the Fama- French three-factor model. Each model measures company risk by measuring the correlation of its stock price to market changes, known as beta. Since estimates of beta are at best imprecise, we rely on peer group betas, rather than individual company betas. Estimating the Market Return Every day, thousands of investors attempt to estimate the market’s expected return. Since the future is unobservable, many practitioners use one of two approaches to estimate it. The first method calculates the cost of equity implied by the relationship between current share prices and future financial performance. By valuing a large sample of companies like the Standard & Poor’s (S&P) 500 index, we can reverse engineer the embedded cost of equity. Although the method requires a forecast of future perfor- mance, it is quite powerful, since it incorporates up-to-date market prices. The second method looks backward using historical market returns. How- ever, given that past market returns are heavily influenced by the rate of in- flation prevalent at the time, a simple average of past returns isn’t helpful in predicting today’s market return. Instead, we add a historical market risk premium (stocks minus bonds) to today’s interest rate, which incorporates today’s expected inflation, rather than past inflation rates. Using Market Prices to Estimate the Cost of Equity  Our first approach— estimating the aggregate cost of equity based on current share prices and ex- pected corporate performance (earnings, return on invested capital [ROIC], and growth expectations) of a large sample of companies—generates striking Estimating the Cost of Equity  309 results. After inflation is stripped out, the expected market return (not excess return) is remarkably constant, averaging 7 percent between 1962 and 2018. To reverse engineer the expected market return, we start with the value driver formula described in Chapter 3. In this case, we’ve expressed it in terms of equity value rather than enterprise value (substituting the cost of equity for the weighted average cost of capital, return on equity for ROIC, etc.): Equity Value Earnings ROE = −     − 1 g k g e where Earnings equity earnings expected growth in earnings ROE expec = = = g ted return on equity cost of equity ke = Solving for the cost of equity gives the following equation: k g g e = −     + Earnings ROE Equity Value 1 Earnings divided by the equity value is the inverse of the price-to-earnings ratio (P/E), so it is possible to further reduce the equation: k g g e =     −    + 1 1 P E ROE / We apply this formula to the S&P 500 index, using the long-run return on equity of 14.5 percent and the long-run growth in real gross domestic product (GDP) of 3.5 percent to convert a given year’s S&P 500 median P/E into the cost of equity.3 Implementing the model is slightly more complex than implied by the formula, because we also strip out the effects of inflation to arrive at a real cost of equity. Exhibit 15.2 plots the real expected market returns between 1962 and 2018. As the exhibit demonstrates, the nominal return changes sub- stantially over time, but the real expected return hovers quite close to 7 percent. For the United Kingdom, the real market return is slightly more volatile and averages 6 percent. Techniques similar to this date back to Charles Dow in the 1920s, and many authors have tested the concept.4 Two studies used analyst forecasts 3 R. Dobbs, T. Koller, and S. Lund, “What Effect Has Quantitative Easing Had on Your Share Price?” McKinsey on Finance, no. 49 (Winter 2014): 15–18; and M. H. Goedhart, T. M. Koller, and Z. D. Williams, “The Real Cost of Equity,” McKinsey on Finance, no. 5 (Autumn 2002): 13–15. 4 E. Fama and K. French, “Dividend Yields and Expected Stock Returns,” Journal of Financial Econom- ics 22, no. 1 (1988): 3–25; R. F. Stambaugh, “Predictive Regressions,” Journal of Financial Economics 54, no. 3 (1999): 375–421; and J. Lewellen, “Predicting Returns with Financial Ratios,” Journal of Financial Economics 74, no. 2 (2004): 209–235.